Question

Jake, Lionel, and Wayne work as house painters for Paint Well Company. Jake can paint 1 room in t hours. Lionel can paint a room 2 hours faster than Jake can. Wayne can paint 2 rooms in 3 times the number of hours that Lionel takes to paint 1 room?

Answer 1

`12/7` hours to paint 1 room if they all work together

Explanation:

`color(red)("You have defined the work rate but not stated the number of rooms"`
`color(red)("to be painted. I will work this out for 1 room and you will have to"`
`color(red)("proportion this up (or down) for however many rooms are needed.")`

For 1 room only:

Jake `->1xxt " room hours"`

Lional`-> 1xx(t-2)" room hours"`

Wayne`->1xx(3(t-2))/2" room hours "larr" 2 rooms in "3(t-2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the time for 1 room if they all work together")`

`t+(t-2)+(3(t-2))/2=1`

`t+t+3/2t-2-6/2=1`

`7/2t=1+2+3`

`t=(2xx6)/7 " hours"`

`t=12/7" hours"larr" For 1 room"`